Combinatorics on permutation tableaux of type A and type B
Copyright policy )Combinatorics on permutation tableaux of type A and type B
We give another bijective proof of a result of Corteel and Nadeau. We find a generating function related to unrestricted columns of permutation tableaux. As a consequence, we obtain a sign-imbalance formula for permutation tableaux. We extend the first bijection of Corteel and Nadeau between permutations and permutation tableaux to type $B$ objects. Using this type $B$ bijection, we generalize a result of Lam and Williams. We prove that the bijection of Corteel and Nadeau and our type $B$ bijection can be expressed as zigzag maps on the alternative representation.
20 pages, 9 figures, final version
- University of Minnesota System United States
- University of Minesota United States
- University of Minnesota-Twin Cities United States
- School of Mathematics University of Minnesota United States
- University of Minnesota United States
Permutations, words, matrices, Combinatorial aspects of partitions of integers, Ferrers diagram, Theoretical Computer Science, Computational Theory and Mathematics, Combinatorial aspects of representation theory, FOS: Mathematics, permutation tableau, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), Combinatorial identities, bijective combinatorics
Permutations, words, matrices, Combinatorial aspects of partitions of integers, Ferrers diagram, Theoretical Computer Science, Computational Theory and Mathematics, Combinatorial aspects of representation theory, FOS: Mathematics, permutation tableau, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), Combinatorial identities, bijective combinatorics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).10 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!